322 research outputs found
Decidability Issues for Petri Nets
This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
Behavioural Equivalence for Infinite SystemsâPartially Decidable!
For finite-state systems non-interleaving equivalences are computationallyat least as hard as interleaving equivalences. In this paper we showthat when moving to infinite-state systems, this situation may changedramatically.We compare standard language equivalence for process description languages with two generalizations based on traditional approaches capturing non-interleaving behaviour, pomsets representing global causal dependency, and locality representing spatial distribution of events.We first study equivalences on Basic Parallel Processes, BPP, a processcalculus equivalent to communication free Petri nets. For this simpleprocess language our two notions of non-interleaving equivalences agree.More interestingly, we show that they are decidable, contrasting a result ofHirshfeld that standard interleaving language equivalence is undecidable.Our result is inspired by a recent result of Esparza and Kiehn, showingthe same phenomenon in the setting of model checking.We follow up investigating to which extent the result extends to largersubsets of CCS and TCSP. We discover a significant difference betweenour non-interleaving equivalences. We show that for a certain non-trivialsubclass of processes between BPP and TCSP, not only are the two equivalences different, but one (locality) is decidable whereas the other (pomsets) is not. The decidability result for locality is proved by a reduction to the reachability problem for Petri nets
Flat counter automata almost everywhere!
This paper argues that flatness appears as a central notion in the
verification of counter automata. A counter automaton is called flat
when its control graph can be ``replaced\u27\u27, equivalently w.r.t.
reachability, by another one with no nested loops.
From a practical view point, we show that flatness is a necessary and
sufficient condition for termination of accelerated symbolic model
checking, a generic semi-algorithmic technique implemented in
successful tools like FAST, LASH or TReX.
From a theoretical view point, we prove that many known semilinear
subclasses of counter automata are flat: reversal bounded counter
machines, lossy vector addition systems with states, reversible Petri nets,
persistent and conflict-free Petri nets, etc. Hence, for these subclasses,
the semilinear reachability set can be computed using a emph{uniform}
accelerated symbolic procedure (whereas previous algorithms were
specifically designed for each subclass)
Membrane Systems with Priority, Dissolution, Promoters and Inhibitors and Time Petri Nets
We continue the investigations on exploring the connection between membrane
systems and time Petri nets already commenced in [4] by extending membrane
systems with promoters/inhibitors, membrane dissolution and priority for rules compared
to the simple symbol-object membrane system. By constructing the simulating
Petri net, we retain one of the main characteristics of the Petri net model, namely, the
firings of the transitions can take place in any order: we do not impose any additional
stipulation on the transition sequences in order to obtain a Petri net model equivalent to
the general Turing machine. Instead, we substantially exploit the gain in computational
strength obtained by the introduction of the timing feature for Petri nets
The 4C spectrum of fundamental behavioral relations for concurrent systems
The design of concurrent software systems, in particular process-aware information systems, involves behavioral modeling at various stages. Recently, approaches to behavioral analysis of such systems have been based on declarative abstractions defined as sets of behavioral relations. However, these relations are typically defined in an ad-hoc manner. In this paper, we address the lack of a systematic exploration of the fundamental relations that can be used to capture the behavior of concurrent systems, i.e., co-occurrence, conflict, causality, and concurrency. Besides the definition of the spectrum of behavioral relations, which we refer to as the 4C spectrum, we also show that our relations give rise to implication lattices. We further provide operationalizations of the proposed relations, starting by proposing techniques for computing relations in unlabeled systems, which are then lifted to become applicable in the context of labeled systems, i.e., systems in which state transitions have semantic annotations. Finally, we report on experimental results on efficiency of the proposed computations
Algorithmic correspondence and completeness in modal logic
Abstract
This thesis takes an algorithmic perspective on the correspondence between modal and hybrid
logics on the one hand, and first-order logic on the other. The canonicity of formulae, and by
implication the completeness of logics, is simultaneously treated.
Modal formulae define second-order conditions on frames which, in some cases, are equiv-
alently reducible to first-order conditions. Modal formulae for which the latter is possible
are called elementary. As is well known, it is algorithmically undecidable whether a given
modal formula defines a first-order frame condition or not. Hence, any attempt at delineating
the class of elementary modal formulae by means of a decidable criterium can only consti-
tute an approximation of this class. Syntactically specified such approximations include the
classes of Sahlqvist and inductive formulae. The approximations we consider take the form
of algorithms.
We develop an algorithm called SQEMA, which computes first-order frame equivalents for
modal formulae, by first transforming them into pure formulae in a reversive hybrid language.
It is shown that this algorithm subsumes the classes of Sahlqvist and inductive formulae, and
that all formulae on which it succeeds are d-persistent (canonical), and hence axiomatize
complete normal modal logics.
SQEMA is extended to polyadic languages, and it is shown that this extension succeeds
on all polyadic inductive formulae. The canonicity result is also transferred.
SQEMA is next extended to hybrid languages. Persistence results with respect to discrete
general frames are obtained for certain of these extensions. The notion of persistence with
respect to strongly descriptive general frames is investigated, and some syntactic sufficient
conditions for such persistence are obtained. SQEMA is adapted to guarantee the persistence
with respect to strongly descriptive frames of the hybrid formulae on which it succeeds, and
hence the completeness of the hybrid logics axiomatized with these formulae. New syntactic
classes of elementary and canonical hybrid formulae are obtained.
Semantic extensions of SQEMA are obtained by replacing the syntactic criterium of nega-
tive/positive polarity, used to determine the applicability of a certain transformation rule, by
its semantic correlateâmonotonicity. In order to guarantee the canonicity of the formulae on
which the thus extended algorithm succeeds, syntactically correct equivalents for monotone
formulae are needed. Different version of Lyndonâs monotonicity theorem, which guarantee
the existence of these equivalents, are proved. Constructive versions of these theorems are
also obtained by means of techniques based on bisimulation quantifiers.
Via the standard second-order translation, the modal elementarity problem can be at-
tacked with any second-order quantifier elimination algorithm. Our treatment of this ap-
proach takes the form of a study of the DLS-algorithm. We partially characterize the for-
mulae on which DLS succeeds in terms of syntactic criteria. It is shown that DLS succeeds
in reducing all Sahlqvist and inductive formulae, and that all modal formulae in a single
propositional variable on which it succeeds are canonical
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